Algebraic techniques for eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic mechanics

Algebraic algorithms for a class of Schrödinger equations in split quaternionic mechanics

“…However, it seems that the discussion and study of the problem of generalized eigenvalues of split quaternion matrices is not limited to complex values. Similar to the eigenvalues of split quaternion matrices [18][19][20][21][22][23], they should theoretically contain other forms of equivalence classes of cases. To this end, we consider the following a common kind of split quaternion generalized eigenvalue problem based on the least squares perspective.…”

Algebraic techniques for eigenvalues and eigenvectors of a nectarine matrix in nectarine algebra

“…Moreover, matrix eigenvalue problems are not only important branches in the field of numerical algebra that can directly solve mathematical computational problems such as optimization and ordinary differential equations, but also fundamental problems in the study of physics and thermodynamics. Until now, the eigenvalue problems of quaternion matrices and split quaternion matrices have been well studied, 21–25 but there are still many gaps in other $$$ {\mathbb{R}}^4 $$$ algebraic fields. In paper, 26 the authors redefined the eigenvectors of matrices of $$$ {\mathbb{R}}^4 $$$ algebras based on invertible elements, and derived the conclusion by a counterexample that a matrix of $$$ {\mathbb{R}}^4 $$$ algebras do not necessarily have eigenvalues even if it is invertible.…”

Iterative Methods for Least Squares Problem in Split Quaternionic Mechanics

“…split quaternionic least squares (SQLS) problem. The main difficulty in solving this problem is the non-commutative and non-skew-field of the split quaternion and the standard mathematical methods(see [4,5,6] and their references) of the complex number field cannot work. In [4], for the first time, the split quaternionic least squares (SQLS) problem was discussed by means of the real representation and the complex representation, which is also main methods for researching the quaternionic least squares (QLS) problem [7,8].…”